The invention relates generally to GPS systems and, in particular, to Kalman filters for use in GPS systems.
A global positioning system (GPS) receiver requires signals from a number of GPS satellites in order to accurately calculate its position. The GPS receiver acquires and tracks signals consisting of carrier, pseudo random codes and modulated data from various satellites. The receiver correlates locally-generated codes with the codes received from the respective satellites, to derive timing information relating the receiver time relative to the local generation of code chips to the satellite time at the times of the transmission of the corresponding code chips. The timing relationship between the receiver time and the transmission times of the signals at the various satellites can be used in conjunction with the modulated data from the respective satellites to generate a position of the receiver with respect to a reference frame shared with the satellites, for example, the earth centered earth fixed (ECEF) frame.
At least 4 satellites are required to provide a GPS position solution. The GPS receiver determines pseudoranges to the respective satellites and associated Doppler rates, and based on these determines its position relative to the satellites. Corrections to pseudorange measurements with respect to a fixed position, which is generated at a xe2x80x9cbase stationxe2x80x9d receiver, can be used to derive a relative position of the local receiver with respect to the base station position. Further, carrier measurements taken at the base station and the local receiver can be mixed in a known manner, to reduce the noise on pseudorange measurements. For example, the carrier measurements associated with a given set of satellites over time may be used to produce carrier-smoothed pseudorange measurements.
The mix of carrier measurements and pseudorange measurements is adversely affected by ionospheric phase advance and multipath. The ionospheric phase advance is equal to and the opposite of the isonospheric group delay, such that over time the change in pseudorange errors deviates from the changes in carrier measurements according to the ionospheric change. Also, pseudorange errors that are corrupted by multipath are biased, such that the combined pseudorange carrier measurement error is difficult to estimate. Further, the carrier measurements from the same set of satellites must be continuously tracked for a sufficiently long time, for example, 100 seconds, to be useful in smoothing, i.e., reducing the noise on, the pseudorange measurements.
It is common for one or more of the GPS satellites to become unavailable to the GPS receiver for various periods of time in, for example, urban environments, when the GPS receiver travels under a bridge, through a tunnel, or through what is referred to in the literature as an xe2x80x9curban canyon,xe2x80x9d in which buildings block the signals or produce excessively large multipath signals that make the satellite signals detrimental to use for position calculations. When tracking of a particular satellite signal is interrupted, the accuracy of the pseudorange measurements reverts back to the unsmoothed level, since the continuous tracking required for carrier-smoothing has been interrupted.
The invention is a GPS receiver that utilizes measurements which span previous and current times, such as delta phase measurements, in a modified Kalman filter. The modified Kalman filter updates position information relating to both the current and the previous times, and propagates the current position and velocity related information. Using both the current and the previous position related information in the filter in conjunction with delta phase measurements, essentially eliminates the effect of system dynamics from the system model, as discussed below, and, a position difference can thus be formed that is directly observable by the phase difference measured between the previous and current time epochs.
The filter requires only that the delta phase measurements be available since the previous time epoch, and not that the same set of satellites be available over the time required, i.e., a series of epochs, for carrier-smoothed pseudorange measurements. Accordingly, the filter provides reduced noise positions even in an environment in which various GPS satellites are available, i.e., visible, to the GPS receiver for relatively short periods of time.
More specifically, the delta phase measurements are incorporated in a Kalman filter that has been modified to update both current and previous position error information. The filter maintains current and previous position error states and current velocity error states, and the Kalman propagation is based on the solution of the differential equations describing the dynamics of the state elements. The dynamics matrix of the filter is based on an assumed constant velocity condition and compensates, at least in part, for measurement errors associated with ionospheric and tropospheric conditions by including process noise that is based on a random walk model. The effect of clock bias in the pseudoranges is removed by differencing pseudoranges across satellites. The effect of clock rate is removed from doppler and carrier measurements by differencing these measurements across satellites. With the effects of clock bias and clock rate removed, the position alone becomes observable with differenced pseudorange measurements, and velocity becomes observable with differenced doppler measurements. The single-differenced phase measurements are then differenced across time, to observe the position change between the previous and current position. In this way, the filter essentially removes the adverse effects of system dynamics from the position calculations, and more accurately estimates position and velocity.
The invention description below refers to the accompanying drawings in which
FIG. 1 is a functional block diagram of a GPS receiver constructed in accordance with the invention; and
FIG. 2 is a functional block diagram of a NovAtel OEM4 GPS receiver that has been modified to include the Kalman filter of the system of FIG. 1.